# Adaptive Model Refinement with Batch Bayesian Sampling for Optimization of Bio-inspired Flow Tailoring

## TL;DR

This paper enhances adaptive surrogate-based optimization by integrating Bayesian sampling to intelligently select sample locations, improving efficiency and effectiveness in complex design problems like bio-inspired flow control.

## Contribution

It introduces AMR-PBS, a novel method combining adaptive model refinement with penalized batch Bayesian sampling for better sample placement in optimization.

## Key findings

- AMR-PBS outperforms Bayesian EGO on benchmark functions.
- The method achieves a 10% drag reduction in flow control design.
- Effective sample placement improves optimization efficiency.

## Abstract

This paper presents an advancement to an approach for model-independent surrogate-based optimization with adaptive batch sampling, known as Adaptive Model Refinement (AMR). While the original AMR method provides unique decisions with regards to "when" to sample and "how many" samples to add (to preserve the credibility of the optimization search process), it did not provide specific direction towards "where" to sample in the design variable space. This paper thus introduces the capability to identify optimum location to add new samples. The location of the infill points is decided by integrating a Gaussian Process-based criteria ("q-EI"), adopted from Bayesian optimization. The consideration of a penalization term to mitigate interaction among samples (in a batch) is crucial to effective integration of the q-EI criteria into AMR. The new AMR method, called AMR with Penalized Batch Bayesian Sampling (AMR-PBS) is tested on benchmark functions, demonstrating better performance compared to Bayesian EGO. In addition, it is successfully applied to design surface riblets for bio-inspired passive flow control (where high-fidelity samples are given by costly RANS CFD simulations), leading to a 10% drag reduction over the corresponding baseline (i.e., riblet-free aerodynamic surface).